Regional indicators

In this example a set of regional indicator variables is added to the model. There are four mutually exclusive regions to consider. A reference group must be chosen, in this case for the northeast. The model becomes:

wage = ві + e2educ + ^ south + S2midwest + 53west + e

where black and female are indicator variables. Taking the expected value of ln(wage) reveals each of the cases considered in the regression

ві + e2educ Northeast

Подпись: E [wage]Подпись: (7.2)ві + ^і + e2educ South ві + $2 + e2educ Midwest ві + $з + e2educ West

Once again, the omitted case (Northeast) becomes the reference group.

The regional dummy variables are added to the wage model for black females and is estimated by least squares. The regional indicator variables are tested jointly for significance using the omit statement.

1 ols wage const educ black female blk_fem south midwest west

2 omit south midwest west

3 series sser = $ess

The results appear below:

Model 4: OLS, using observations 1-1000
Dependent variable: wage

Coefficient

Std. Error

t-ratio

p-value

const

-5.28116

1.90047

-2.7789

0.0056

educ

2.07039

0.134878

15.3501

0.0000

black

-4.16908

1.77471

-2.3492

0.0190

female

-4.78461

0.773414

-6.1863

0.0000

blk_fem

3.84429

2.32765

1.6516

0.0989

Mean dependent var 20.61566 S. D. dependent var 12.83472

Sum squared resid 130194.7 S. E. of regression 11.43892

R2 0.208858 Adjusted R2 0.205677

F(4,995) 65.66879 P-value(F) 2.53e-49

Log-likelihood -3853.454 Akaike criterion 7716.908

Schwarz criterion 7741.447 Hannan-Quinn 7726.234

First, notice that the sum-of-squared errors has been saved for future use. The only regional indicator that is individually significant at 5% is midwest. The joint test results are

Comparison of Model 3 and Model 4:

Null hypothesis: the regression parameters are zero for the variables south, midwest, west

Test statistic: F(3, 992) = 4.24557, with p-value = 0.00542762 Of the 3 model selection statistics, 1 has improved.

The test statistic has an F(3, 992) distribution under the null and is equal to 4.25. The p-value is less than 5% and we conclude that the indicators are jointly significant.

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